In my aforesaid copending application, I disclose a convertible seat-bed unit in which a back is moved from an inclined position downwardly to a position behind a seat, the seat being moved forwardly, and the back and the seat then having upper surfaces substantially in a common horizontal plane for use as a bed. As also disclosed, a linkage arrangement is provided for effecting the proper conjoint movement of the seat and the back in a manner such that the top edge portion of the back is moved substantially in a vertical path. No forward movement of the supporting frame is required in changing from the seat condition to the bed condition and the arrangement is especially advantageous in camper vehicles or the like in which the supporting frame can be rigidly secured to the frame of the vehicle.